A particle is moving in a conservative force field from point A to point `B.U_(A)` and `U_(B)` are the potential energies of the particle at point A and B and `W_(C)` is the work done by conservative forces in the process of taking the particle from A and B, which of the following is true?

Options

A. `W_(c)=U_(B)-U_(A)`
B. `W_(C)=U_(A)-U_(B)`
C. `U_(A) gt U_(B)`
D. `U_(B) gt U_(A)`

Explanation

To solve the problem, we need to analyze the relationship between the work done by conservative forces and the potential energy at two points in a conservative force field.

### Step-by-Step Solution:

1. **Understanding the Concept of Conservative Forces**:
- Conservative forces are forces for which the work done is independent of the path taken and depends only on the initial and final positions. The work done by conservative forces is related to the change in potential energy.

2. **Identifying the Given Information**:
- Let \( U_A \) be the potential energy at point A.
- Let \( U_B \) be the potential energy at point B.
- Let \( W_C \) be the work done by conservative forces when moving from point A to point B.

3. **Applying the Work-Energy Principle**:
- The work done by conservative forces can be expressed as the change in potential energy:
\[ W_C = U_A - U_B \]
- This equation indicates that the work done by the conservative force is equal to the initial potential energy minus the final potential energy.

4. **Rearranging the Equation**:
- From the equation \( W_C = U_A - U_B \), we can also express it as:
\[ W_C = U_B - U_A \]
- However, this would imply a negative work done if \( U_B \) is greater than \( U_A \).

5. **Analyzing the Options**:
- Option 1: \( W_C = U_B - U_A \) - This is incorrect based on our derived equation.
- Option 2: \( W_C = U_A - U_B \) - This is correct as per our derivation.
- Option 3: \( U_A > U_B \) - This is not necessarily true; it depends on the specific values of potential energy.
- Option 4: \( U_B > U_A \) - This is also not necessarily true; it depends on the specific values of potential energy.

6. **Conclusion**:
- The correct statement is:
\[ W_C = U_A - U_B \]
- Therefore, the correct option is Option 2.